Power Plant Valuation
over a 1-year horizon on an ordinary computer. Solution approach 2 can be carried out with a single model
run, but overall it is generally more time consuming. The reason is that we expand the state-space by a factor of NMax, where NMax equals the number of allowed starts per year: whereas the original dimensions in the previous example are 8,760 x 4, they now become 8,760 x 4 x 50 when, for example, 50 starts are allowed. Multiplying the dimensions gives the number of ‘nodes’ in the state-space: from each node the model decides which other node in the next hour is optimal. Continuing the previous example, and assuming we already started 20 times before (N=20), the choice is:
max { t+1
nodes. The regression is carried out on simulated price levels at time t, which are here denoted by S(t) and P(t). In our implementation we use the current spark spread as S(t) and the average spark spread over the past 24 hours as P(t). Additional price information, such as the forward spark spread, may be incorporated to improve the estimate, but our analysis suggests this hardly improves the performance. However, this whole process takes quite some time, making the model roughly 10 times slower than with approach 2 and roughly 50 times slower than with approach 1. This is the price we pay for avoiding perfect foresight.
F on 1hr, N=21 + Margin t+1 – Start Costs t+1 – Shadow Costs F off 2h, N = 20
t+1 The time-consuming part is that this type of calculation needs
to be performed for each N = 0 to 49. Solution approach 3 is Least-Squares Monte Carlo. The
general idea is to estimate the values at the different nodes, instead of assuming perfect knowledge about the true value. Longstaff and Schwartz (2001) made this approach popular and it is a key algorithm in many KYOS applications. In the above example and a maximum of 50 starts, the model carries out 8,760 x 4 x 50 individual linear regressions (‘least squares’) to estimate the values at the node. For example, in order to estimate F on 1hr N=21 at (t+1) the continuation value it is based on a regression estimate, which may take the following form:
F on 1hr N=21 = α + β1 . St + β2 . St2 t+1
+ γ1 . Pt + γ2 . Pt2
This equation is estimated at each node, so in our example we get different parameters for each of the 8,760 x 4 x 50
“Plant switched on in hour t+1” “Plant remains off in hour t+1”
Case Description Developing
the
above solutions is a considerable effort. The question is whether this
pays off in better insights when comparing different investment options. Furthermore, the question is whether the additional calculation time of the Least-Squares Monte Carlo method leads to fundamentally new outcomes. In order to verify this, we consider a power plant over
the year 2011 in the UK market. As a first step, we generate Monte Carlo simulations over 2011, using KYOS’ model KySim as we did for our study last year. The model incorporates cointegration and a multi-commodity and multi-factor model for the forward curve movements. It is also based on a regime- switches and cointegration for spot prices. The CCGT plant under consideration has a maximum output of 860 MW at an efficiency of 57.5%. When spark spreads are negative, the plant can reduce its
output to the minimum stable level of 510 MW at an efficiency of 54.5%. It can also turn off the production and restart at a later point in time. In the base case the plant can start and stop without any limitation and without any start costs. Based on a single scenario (the hourly forward curves), the optimal
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